Assuming you're an engineer, have you thought about what handing over a "window" from one computer to another actually entails? CRIU can do checkpoint/restore at container/process level - but you actually want it to run on both, no? So you need to split off just the I/O, but at the OS-level per window.
Apple has been doing a lot of work in this direction and they have stuff that actually work (like video calls and to some extent windows. These are processes running on different OS-es with a matrix of hundreds of devices.
It's not something you vibe code over the weekend.